> If you tune with exact 2^(1/12) semitones then all your octaves will be in tune for obvious reasons. Hypothetically, or on an electronic instrument, you coul

> If you tune with exact 2^(1/12) semitones then all your octaves will be in tune for obvious reasons. Hypothetically, or on an electronic instrument, you could. But if you did all 2^(1/12) ratios, your octaves wouldn't be in tune. Strings on a piano do not behave like an ideal string. Their overtones are not 2X, 3X, 4X, 5X, etc. times the fundamental frequency. Instead, the actual overtones are higher than the ideal frequencies. This is called inharmonicity (https://en.wikipedia.org/wiki/Inharmonicity https://en.wikipedia.org/wiki/Inharmonicity). So when tuning a piano, you have to tailor the way you tune it to each different piano if you want that piano's lower strings to be in tune with its higher strings.